Higher genus capillary surfaces in the unit ball of R-3

Abstract

We construct the first examples of capillary surfaces of positive genus, embedded in the unit ball of R-3 with vanishing mean curvature and locally constant contact angles along their three boundary curves. These surfaces come in families depending on one parameter and they converge to the triple equatorial disk. Such surfaces are obtained by deforming the Costa-Hoffman-Meeks minimal surfaces.